Regular black holes in Verlinde's emergent gravity

TL;DR

This paper constructs and analyzes a variety of regular black hole solutions within Verlinde's Emergent Gravity, exploring their geometries, effects of apparent dark matter, and extensions to rotating and cosmological constant scenarios.

Contribution

It introduces new regular black hole solutions in VEG, including various types and their properties, and develops methods to incorporate rotation and cosmological constant effects.

Findings

Apparent dark matter causes non-asymptotically flat geometries.

Special limits recover monopole-like solutions with deficit angles.

Extended solutions include rotating and de Sitter cases.

Abstract

In this paper, we construct a class of charged and regular black hole solutions in Verlinde's Emergent Gravity (VEG). In particular, these solutions include, black holes with asymptotically Minkowski core, T-duality, Frolov/Simpson-Visser type solutions, as well as the Bardeen/Hayward type solutions as a special case. Using the relation between the apparent dark matter and the baryonic matter we find the effect of apparent dark matter on the spacetime geometry. We show that in general, the apparent dark matter leads to non-asymptotically flat spacetime geometry and, in the special limit of a point like mass distribution, all the black hole solutions in VEG resembles the global monopole-like solution with a deficit angle. To this end, we extend the solutions by including the cosmological constant (de Sitter space) and we elaborate different energy conditions of black hole solutions. Finally, having in mind that the Einstein's field equation are not modified in this theory while the apparent dark matter is encoded in the energy-momentum tensor, we used the modified Newman--Janis-Azreg-A\"inou algorithm to obtain the corresponding effective rotating metrics.